The Consensus of Subjective Probability Distributions

By Robert L. Winkler. 1968

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination (2012, background): “The study of distributed control of multiple vehicles was pe rhaps first motivated by the work in distributed computing [ 1], management science [ 2], [3], and statistical physics [ 4].”
Probability Aggregation Methods in Geoscience (2012, methodology): “In the context of aggregating expert opinion, Winkler (1968) suggests four ways of assessing the weights for the linear pool, which could also be applied to the other methods: (i) equal weights; (ii) weights proportional to a ranking based on expert’s advice; (iii) weights proportional to a…”
Combining Predictive Distributions (2011, methodology): “…are available (Genest and Zidek 1986; Clemen and Winkler 1999; 2007), the linear pool is typically the method of choice, with the pioneering work of Winkler (1968) and Zarnowitz (1969), and recent papers by Mitchell and Hall (2005), Wallis (2005), Hall and Mitchell (2007), Jore, Mitchell and Vahey…”
Reaching a Consensus (1974, background): “The author is indebted to Robert Winkler, Stephen Fienberg, Dennis Lindley, James Patell, S. James Press, Scott Richard, and members of the NBER-NSF Seminar on Bayesian Inference in Econometrics for their helpful comments, and to Carolyn Pugh for her secretarial assistance. distribution over Q for w”
Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks (2012, background): “The study of consensus algorithms can be dated back to Winkler (1968) and DeGroot (1974).”
Decision analysis in Management Science (2004, background): “Winkler (1968MS) was one of the first to consider the problem and compared weighted averages and a Bayesian approach based on the use of natural conjugate distributions.”
Combining forecasts: A review and annotated bibliography (1989, unknown): “Contributions include axiomatic work (e.g., Madansky, 1964; McConway , 1981; Lehrer and Wagner, 1981) as well as Bayesian treatments (e.g., Winkler, 1968; De- Groot, 1974).”
Combining forecasts – forty years later (2011, background): “…Zidek (1986, p. 119) suggests that Winkler (1968) earlier referred to the logarithmic opinion pool, and later authors, for example Kascha and Ravazzolo (2010, pp. 233, 237), similarly reference Winkler (1968), but this is not correct: Winkler (1968) does not mention the logarithmic opinion pool.”
Sentiment analysis of blogs by combining lexical knowledge with text classification (2009, methodology): “There is a substantial literature on the mathematical combination of probability distributions, including reviews such as Winkler [30], Genest and Zidek [11], and French [10].”
Distributed Coordination of Networked Fractional-Order Systems (2010, background): “As for a group behavior, sharing information with each other or consulting more than one expert, as stated in [1], makes the decision makers more confident.”
Coordination and Consensus of Networked Agents with Noisy Measurements: Stochastic Algorithms and Asymptotic Behavior (2009, background): “We mention that there has been a long history of research on consensus problems due to the broad connections of this subject with a wide range of disciplines including statistical decision theory, management science, distributed computing, ad hoc networks, biology [49, 20, 10, 18, 28, 26, 48], and t”
The Evolution of Forecast Density Combinations in Economics (2018, methodology): “Management science and risk analysis The combination of predictive densities has received considerable attention within management science and risk analysis dating back, at least, to Winkler (1968); for reviews see Genest and Zidek (1986) and Clemen and Winkler (1999).”
A tutorial on modeling and analysis of dynamic social networks. Part I (2017, methodology): “Unlike [83, 86], the DeGroot procedure was a decentralized algorithm: each agent modifies its opinion independently based on the opinions of several “trusted” individuals, and there may be no agent aware of the opinions of the whole group.”
Forecast combinations: An over 50-year review (2022, methodology): “…integrated into the individual distributions; and (ii) if not, the extra knowledge from the decision maker can be incorporated in the likelihood as an additional individual distribution; see, e.g., Winkler (1968), Clemen and Winkler (1993), Clemen and Winkler (1985), and Jouini and Clemen (1996).”
Combining inflation density forecasts (2010, methodology): “Winkler (1968) points out that the logarithmic opinion pool has a natural-conjugate interpretation.”